Based on the sparsity of the angular cascaded channel, the cascaded channel estimation problem can be also formulated as a sparse signal recovery problem [1]}. Then, some classical CS algorithms, such as orthogonal matching pursuit (OMP), can be directly used to estimate the angular cascaded channel with reduced pilot overhead. However, these conventional CS algorithms cannot achieve the satisfying estimation accuracy, especially in low SNR ranges. In order to improve the estimation accuracy, a joint sparse matrix recovery based channel estimation scheme was proposed in [2]}. In this scheme, all angular channels associated with different users can be projected to the same subspace by considering the fact that different users enjoy the same channel \(\bf {G}\)  from the RIS to the BS. However, for these sparsity based channel estimation schemes [1]}, [2]}, the required pilot overhead is still high, since the sparsity of the angular cascaded channel becomes less significant compared with the angular channel in conventional communications.
